Invited Session Tue.2.H 0112

Tuesday, 13:15 - 14:45 h, Room: H 0112

Cluster 16: Nonlinear programming [...]

Real-time optimization II


Chair: Victor M. Zavala and Sebastian Sager



Tuesday, 13:15 - 13:40 h, Room: H 0112, Talk 1

Mihai Anitescu
Scalable dynamic optimization

Coauthor: Victor Zavala


In this talk, we discuss scalability issues arising in dynamic optimization problems such as model predictive control and data assimilation. We present potential strategies to avoid them, where we focus on scalable algorithms for methods that can track the optimal manifold with even one quadratic program per step. This builds on recent work of the authors where we proved using a generalized equations framework that such methods stabilize model predictive control formulation even when they have explicit inequality constraints. In particular, we present alternatives to enable fast active-set detection and matrix-free implementations.



Tuesday, 13:45 - 14:10 h, Room: H 0112, Talk 2

Christian Kirches
A real-time iteration scheme for mixed-integer nonlinear model predictive control

Coauthors: Hans-Georg Bock, Sebastian Sager


A class of nonlinear model predictive control problems with both continuous and binary controls is considered. Partial outer convexification and relaxation is used to obtain a continuous model predictive control problem with possibly increased control dimension. The problem can then be solved by combining a direct method for optimal control with a rounding scheme. Feasibility and comptimality certificates hold, while numerical computations typically do not
involve an exponential runtime effort. It is argued that the idea of real-time iterations proposed by Diehl et al. can be used to devise a new mixed-integer real-time iteration scheme for this problem class. To this end, it is shown that adding a rounding step to one iteration of the scheme can be interpreted as carrying out a step of an perturbed Newton-type method. Sufficient conditions for local contractivity of such a perturbed method are derived. Based on this local contractivity argument, a proof of locally asymptotic convergence of the proposed scheme on a receeding horizon is given for the nonlinear discrete-time case. An upper bound on the allowable sampling time of the scheme and on the loss of optimality is derived.



Tuesday, 14:15 - 14:40 h, Room: H 0112, Talk 3

Francesco Borrelli
Real-time stochastic predictive control applied to building control systems

Coauthors: Matusko Jadranko, Yudong Ma


The presentation will focus on the solution of linear
stochastic model predictive control (SMPC) subject to joint
chance constraints. We present and compare two approaches.
In the the explicit approach a set of unknowns representing allowable violation for each constraint (the risk) is introduced. A tailored interior point method is proposed to explore the special structure of the resulting SMPC problem computing the input sequence and the risk allocation. In the sample-based approach, a large number of stochastic samples is used to transform the SMPC problem into a deterministic one with the original constraints evaluated in every sample. The proposed methods are applied to a building control problem which minimizes energy usage while keeping zone thermal comfort by using uncertain prediction of thermal loads and ambient temperature. Extensive numerical and experimental tests are use to analyze the conservatism and the effectiveness of the proposed approaches.


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